UV mapping a Logo on Specific face of object
The distribution of the material has nothing to do with the UV layout. You have 3 material slots, 2 of which are empty and apparently not assigned to anything. 
Go into edit mode select everything, assign a material to the 1. slot and press assign. 
Then select only the face the logo is supposed to be on, select the 2. slot and press assign. 
That will fix it in your case, but best practice is to keep it in one material, use a 2. UVLayout just for the logo and mix it in with your main texture (or color).